The interaction of 4′-(N,N-dimethylamino)-6-hydroxyflavylium cation with double stranded (ds-) DNA/RNA was studied by UV/Vis spectrophotometry, circular dichroism (CD), and also steady-state and time-resolved emission spectroscopies at neutral and weakly acidic conditions. At pH 5, the studied molecule, in its flavylium cationic form, showed considerable binding affinities (5 < logKs < 6) for all ds-DNA/RNA, contrary to chalcones forms (dominant at pH 7), which did not show binding to polynucleotides. Flavylium cation intercalated into ds-DNAs at variance to dominant groove aggregation within ds-RNA, which was reported by RNA-specific bisignate induced CD spectrum (ICD) bands. The intrinsically negligible fluorescence of flavylium was strongly increased upon the addition of DNA or RNA, whereby both the fluorescence intensity and emission lifetimes of complexes differed considerably: the strongest emission increase was observed for AU-RNA (detection limit estimated to 10 nM) followed by AT-DNAs and the much weaker effect of GC-DNAs. Both fluorescence sensitivity on the ds-DNA/RNA secondary structure and sequence-selective ICD bands make the flavylium–chalcones system an intriguing pH-switchable new probe for distinguishing between various polynucleotide sequences.